Well-posedness of the two-phase flow problem. Part 1. Stability analysis procedures discussed and applied to the equal-pressures model
A certain two-phase flow model assumes equal pressures in the two phases. This study refers to that model as the equal-pressures model. The validity of the equal-pressures model has been questioned. One way to check on the validity of this model is to see if it leads to a well-posed problem. The analysis presented herein suggests that the equal-pressures model does not lead to a well-posed problem. This leads to the suspicion that the equal-pressures model does not model the behavior of two-phase flow very well. This report also discusses methods of analyzing the well-posedness of problems of this type. A point of difficulty is whether or not a von Neumann stability analysis can prove anything about well-posedness for nonlinear problems. In the case of the transient, pure initial-value problem for systems of linear PDE's (Partial Differential Equations) with constant coefficients, it can be proved that von Neumann stability is equivalent to well-posedness. Apparently no one has proved a similar result applicable to the nonlinear case at hand. However, it is generally believed that if a model is unstable in the sense of von Neumann then that model does not lead to well-posed problems. This report presents a proof that the equal-pressures model is unstable in the sense of von Neumann.
- Research Organization:
- Sandia Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 5857160
- Report Number(s):
- SAND-79-1435
- Country of Publication:
- United States
- Language:
- English
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